G0 G1 G2 G3 Continuity in Surfacing
MATHI KRISHNAN
he Gx designations describe the relationship between the adjoining faces of two surface that share a common edge.
* In the case where two surface share a common edge but the adjoining faces are NOT smooth or continuous, it's said that these surfaces are G0 continuous.
* In the case where two surface share a common edge and the adjoining faces are tangent, it's said that these surfaces are G1 continuous.
* In the case where two surface share a common edge and the adjoining faces are curvature continuous, it's said that these surfaces are G2 continuous.
* And there's even a case where if two surface share a common edge and the adjoining faces have the same rate of change of curvature, or acceleration,
it's said that these surfaces are G3 continuous.
G0 means the ends or edges of curves or surfaces will meet the curve or surface that they are G0 with.
They can meet at any angle and have a G0 condition just so long as the two surfaces or curves touch either at the endpoints or edges respectively.
This condition allows surfaces to be sewn or curves to form closed loop which will allow you to create solids for example.
G1 means tangency,Within the dialogs it is generally the case the G1 also implies or imparts a G0 condition and so on.
For tangency the first control point will align with the slope of the base geometry at the point where they meet. You need to get into control polygons
a little to understand how curves and surfaces are built in CAD. Tangency is necessary to building good models in order to have blends and other swept
geometry be constructed successfully. In fact the most common tangent features are corner radii or radius blends on surfaces or solids.
In general engineering models require this basic level of smoothness it describes formed processes, provides for mold flow and promotes good
structural integrity, (lack of stress raisers or fault lines).
G2 is the first real continuity condition it is described in terms of knot points by the two nearest the end aligning with two on the opposite base curve
or surface. It means that they have the same curvature locally where the ends meet. The difference between a radius that is tangent and circular
in section and an edge blend that is curvature continuous is largely aesthetic.
Light strikes a radius the point of tangency departure near the edges of the radius often showing as two highlights on either side of the center of
the radius. A curvature continuous blend can be controlled so that the light strikes the surface as a single highlight at or near the apex of the blend,
depending on how it is built. For styling purposes this is far superior and throughout the whole model edge conditions need to be continuous if light
is to fall on highly reflective surfaces so that the product has pleasing highlights. This is in fact called highlighting and is used extensively
in automotive and industrial design applications. In those circles the surfaces are usually referred to as A-class.
G3 is one better than G2 for surface continuity. It allows more control to reach further into the surfaces from the edges. Not only is the curvature
continuous but the rate of curvature continuity is also said to be continuous. In practical purposes three control points re aligned and the degree
of shape control is extended by that much. When used for A-class surfacing it allows surfaces including blends at the edges to be lead in a long way
with a high degree of control over the results. Leading in means setting back the edges a lot further from the corners
(these edges would be tangent lines of radius blends and are still widely referred to as such). In most cases the increased control provides better
smoothness which hopefully translates to better highlights and improved styling.
Types of continuity
Continuity is a mathematical indication of the smoothness of the flow between two curves or surfaces.
The following lists the five types of continuity possible with Alias tools, G0 to G4. Note that G3 and G4 continuity are only available with blend curves.
Tangent (G1)
Same as positional continuity, plus the end tangents match at the common endpoint. The two curves appear to be traveling in the same direction at the join, but they may still have very different apparent “speeds” (rate of change of the direction, also called curvature).
For example, in the illustration at left, the two curves have the same tangent (the double-arrow line) at the join (the dot). But the curve to the left of the join has a slow (low) curvature at the join, while the curve to the right of the join has a fast (high) curvature at the join.
